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Using COMSOL Multiphysics Capability for Engineering High Q MEMS Resonators

Amy Duwel
Charles Stark Draper Laboratory
Cambridge, USA

Micromechanical resonators are used in a wide variety of applications, including inertial sensing, chemical and biological sensing, acoustic sensing, and microwave transceivers. Despite the distinct design requirements for each of these applications, a ubiquitous resonator performance parameter emerges. This is the resonator’s Quality factor (Q), which describes the mechanical energy damping. In all applications, it is important to have design control over this parameter, and in most cases, it is invaluable to minimize the damping. Over the past decade, both experimental and theoretical studies have highlighted the important role of thermoelastic damping (TED) in micromechanical resonators. In this talk, we show how COMSOL Multiphysics was used to explore the fundamental mechanism of thermoelastic damping in MEMS resonators.

Our first approach uses the eigenvalues and eigenvectors of the un-coupled thermal and mechanical dynamics equations to calculate damping. We find that a spatial overlap of thermal modes with the strain profile in the mechanical mode of interest is a dominant term in the damping. In addition, the frequency separation between relevant thermal modes and the mechanical resonance frequency must be considered.

This talk next demonstrates the use of COMSOL Multiphysics to solve the fully coupled thermo-mechanical equations that capture the physics of thermoelastic damping in both two and three dimensions for arbitrary structures. The fully coupled simulations enable a precise evaluation of Q. We derive both 3D equations, as well as 2D plane stress thermoelastic equations. This software can parameterize the material parameters and geometry, so that detailed optimization studies are enabled. We calculate damping in typical micromechanical resonator structures using COMSOL Multiphysics and compare the results with experimental data reported in literature for these devices.

Keynote speaker's biography:
Amy Duwel is currently the MEMS (Micro-Electro-Mechanical Systems) Group Leader at Draper Laboratory and Principal Member of the Technical Staff. Amy leads a new project at Draper on using radioisotope sources to power a MEMS-scale battery. She initiated and leads the RF MEMS effort at Draper, which is focused on high frequency resonator development. She has played a leading role in the modeling and development of MEMS gyros and other inertial sensors at Draper. Her technical interests focus on micro-scale energy transport, and on the dynamics of MEMS resonators in application as inertial sensors, RF filters, and chemical detectors. She has advised several thesis students in collaboration with MIT. Amy was recently named as one of the Top 10 Women to Watch in New England by Mass High Tech. She received a BA in physics from the Johns Hopkins University in 1993. Her MS (1995) and PhD (1999) are in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology.

Amy Duwel was one of the keynote speakers at the COMSOL User's Conference, fall 2005 in Boston